This is a recurring problem with the Non-Unibody MacBooks, and Apple covers this even if you MacBook is out of warranty. The same thing happened to mine about 2 months ago, and I only had to pay labor costs. I live about 2 hours from an Apple Store so I had to take mine to an Apple Service Provider, they covered the part and I just paid for labor. I'm not for sure if Apple Store's charge for labor but I know Service Providers do.
If you're like me and don't live close to an Apple Store and don't know where a Service Provider might be, here is a link to find one.
apple.com/buy/locator/service/